Electronic Journal of Differential Equations (Sep 2013)
Stokes problem with several types of boundary conditions in an exterior domain
Abstract
In this article, we solve the Stokes problem in an exterior domain of $\mathbb{R}^{3}$, with non-standard boundary conditions. Our approach uses weighted Sobolev spaces to prove the existence, uniqueness of weak and strong solutions. This work is based on the vector potentials studied in [7] for exterior domains, and in [1] for bounded domains. This problem is well known in the classical Sobolev spaces $ W ^{m,2}(\Omega)$ when $\Omega$ is bounded; see [3,4].